The constellations that we saw at night half a year ago are now overhead in the daytime. Six months later they will again adorn the night sky. The sunlit atmosphere of the Earth screens them from the eye because the air particles-disperse the sun-rays more than the rays emitted by the stars. (The observer located on the top of a high mountain, with the densest and dustiest layers of- the atmosphere below, would see the brighter stars even in daytime. For instance, from the top of Mt. Ararat (5 km. high), first-magnitude stars are clearly distinguished at 2 o’clock in the afternoon; the sky is seen as having a dark blue colour.)
The following simple experiment will help explain why the stars disappear in daylight. Punch a few holes in one of the sides of a cardboard box, taking care, however, to make them resemble a familiar constellation. Having done so, glue a sheet of white paper on the outside. Place a light inside the box and take it into a dark room; lit from the inside; the holes, representing stars in the   night sky, are clearly seen. But, switch on a light in the room without extinguishing the light in the box and, lo, the artificial stars on our sheet of paper vanish without trace: “daylight” has extinguished them.
One often reads of stars being seen even in daylight from the bottom of deep mines and wells, of tall chimney-stacks and so on. Recently, however, this viewpoint, which had the backing of eminent names, was put to test and found wanting.  As a matter of   fact, none of the men who wrote on this subject, whether the Aristotle of antiquity or 19th-century Herschel, had ever bothered to observe the stars in these conditions. They quoted the testimony of a third person. But the unwisdom of relying on the testimony of
“eye-witnesses,” say in this particular field, is emphasized by the; following example. An article in an American magazine described daylight visibility of stars from the. bottom of a well as a fable. This was hotly contested by a farmer who claimed that he had seen Capella: and Algol in daytime from the floor of a  20-metre high silo. But when his claim was checked it was found that on the latitude of his farm neither of the stars was at zenith at the given date and, consequently could not have been seen from
the bottom of the silo.
Theoretically, there is no reason why a mine or a well should help in daylight observation of stars. We have already mentioned that the stars are not seen in daytime because sunlight extinguishes them. This holds also for the eye of the observer at the bottom of a mine. All that is subtracted in this case- is the light from the sides. All the particles in the layer of air above the surface of the mine continue to give off light and, consequently, bar the stars to vision.
What is of importance here is that the walls of the well protect the; eye from the bright sunlight; this, however, merely facilitates observation of the bright planets, but not the stars. The reason why stars are seen through the telescope in daylight is not because they are seen from “the bottom of a tube,” as many think, but because the refraction of light, by the lens or its reflection in the mirrors detracts from the brilliancy of the part of the sky under observation, and at the same time enhances the brilliancy of the stars (seen as points of light). We can see first-magnitude and even second-magnitude stars in daytime through a 7 cm. telescope. What has been said, however, does not hold true for either wells, mines, or chimneys.
The bright planets, say, Venus, Jupiter or Mars, in opposition, present a totally different picture. They shine far more brilliantly than the stars, and for this reason, given favourable conditions, can be seen in daylight.
From Astronomy for Entertainment – Yakov Perelman Pg: 135-137
Available here.